The radial GF corresponding to the different BC are denoted by \(p_{\text{free}}\) , \(p_{\text{abs}}\) , \(p_{\text{ref}}\) , \(p_{\text{rad}}\)  and \(p_{\text{rev}}\)  and will play a prominent role in the algorithm we will discuss in the following.
For later use, we provide the expressions for \(p_{\text{rad}}\)  in 3D [1]} and \(p_{\text{rev}}\)  in 2D [2]}
\(&&p_{\text{rad}}(r, t\vert t_{0}) = \frac{1}{ 8\pi r r_{0}}\frac{1}{\sqrt{\pi D t}}\bigg [\exp \left[-\frac{(r-r_{0})^{2}}{4Dt}\right] + \exp \left[-\frac{(r + r_{0} - 2a)^{2}}{4Dt}\right] \nonumber \\& & -\kappa \sqrt{4\pi Dt}\exp \left(\kappa ^{2}Dt + (r+r_{0} - 2a)\kappa \right)\text{erfc}\left( \kappa \sqrt{Dt} + \frac{(r+r_{0} - 2a)}{2\sqrt{Dt}}\right)\bigg ], \quad \quad \\& & p_{\text{rev}}(r, t\vert t_{0}) = \frac{1}{2\pi }\int ^{\infty }_{0}e^{-Dtx^{2}}T(r,x)T(r_{0}, x)x \,dx, \) 
